The Labouchère (Cancellation) Roulette System, Worked Through in C$

Most betting systems hide their target. The Labouchère writes it down. Before the first spin you put a short line of numbers on paper, say 1-2-3-4, and those numbers add up to exactly what you are trying to win: 10 units, or C$50 at C$5 a unit. Every bet after that is an attempt to cross the line out.

That written-down quality gives the system its fans. It feels organised, it adapts to the run of the wheel, and it needs far fewer wins than losses to finish. All of which is true, and none of which touches the 2.70% that a single-zero wheel takes from each stake. Like every system on our roulette strategy hub, it rearranges results without changing the price.

The rules, step by step

1. Write a line of numbers. The total is your target in units. 1-2-3-4 is the classic start.
2. Bet the first number plus the last number, in units, on an even-money outcome such as red.
3. If you win, cross off the first and last numbers.
4. If you lose, add the amount you just lost (in units) to the end of the line.
5. When one number is left, bet that number. When none are left, the cycle is complete and you are up by the target.

Players often say the system needs “one win for every two losses”. That is close: every win removes two numbers, every loss adds one.

A winning cycle in Canadian dollars

Here is the 1-2-3-4 line at C$5 a unit, with four wins and three losses:

Seven bets, three of them losses, and the line is gone with exactly C$50 profit, the total of the original 1-2-3-4. You can check the bookkeeping another way: the four wins paid C$30 + C$50 + C$45 + C$20 = C$145, the three losses cost C$25 + C$30 + C$40 = C$95, and C$145 minus C$95 is C$50.

Spin five is worth a second look. Down C$65, you bet C$50 on the strength of a line that had grown to five numbers. The system dragged the stake up to twice the first bet within four spins. That is the mild version of what happens on a worse run.

A losing run

Now take six even-money losses in a row from the same start:

After six losses the line runs from 1 to 10, adds up to 55 units, and the next bet is 11 units or C$55. You are C$225 down chasing what is now a C$275 line, and the target is still the same C$50 above where you started. Straight losing runs like this one are rare (six in a row has a probability of about 1.83%), but choppy runs with more losses than wins push the line out in the same direction, just more slowly.

The line gets longer one number per loss, and its middle numbers never get bet until the ends are cleared. That is why a long Labouchère line feels as if it will never close.

How often a cycle fails

Because a win clears two numbers and a loss adds only one, you need to win only a little over a third of your bets to finish a line. An even-money bet wins 18 times in 37, roughly 48.6%, so most cycles complete. The question is what the others cost.

We ran 400,000 cycles of the 1-2-3-4 line at C$5 a unit on a European wheel, stopping a cycle when the next bet would be more than C$500, a common table maximum:

Twenty-two completed cycles earn about C$1,100. One failed cycle wipes that out and more. The average over all cycles was a loss of C$18.12, and the average cycle staked C$669.34, of which 2.70% is C$18.09. The match is no coincidence: the edge on each bet is all that decides the long-run result.

With a personal ceiling as well, the failures come sooner and hurt less. If you stop a cycle whenever the next bet would take your losses past C$500, 87.3% of cycles complete and the rest end with an average loss of about C$419. Fewer disasters, more small ones, the same price.

Why the price stays at 2.70%

A Labouchère stake is still a plain even-money bet that costs, on average, one thirty-seventh of itself. The line decides how big each stake is, and the wheel decides the odds. Write any line you like, long or short, conservative or aggressive, and the expected result of a session remains the total staked times minus 2.70%. The roulette odds calculator shows the same figure for any single bet in the table above.

That makes the system’s real effect easy to state. It makes winning cycles very common and losing cycles very expensive. Plenty of players find that trade enjoyable. It just should not be mistaken for an advantage.

Why a written line feels so convincing

There is a reason the Labouchère has kept its following for well over a century. It turns an evening at the wheel into a task with visible progress. Each win puts a line through two numbers, the list gets shorter, and the end is always in sight. A losing spin only adds one number at the back, so even a bad patch looks manageable on paper.

The paper hides the one figure that matters, which is how much money the line now represents. A line reading 2-3-4-6-8 looks like five small numbers. At C$5 a unit it is C$115 still to be covered, on top of whatever has already been lost, and the next bet is C$50. Players who keep the line in their head tend to underestimate this badly. If you play the system, write the running total next to the line after every spin. It is the most useful habit the method can have, and it makes the point at which to stop much easier to see.

A second trap is the target itself. Because the line promises a fixed amount, a session can start to feel unfinished until it is complete, even when the money set aside is gone. Nothing about the line entitles it to your next deposit. An uncompleted line is simply a session that ended where it ended.

The Labouchère on dozens and columns

The standard rules assume an even-money bet. Some players run the line on a dozen or a column instead, which pays 2 to 1. Two things change. Now a winning bet pays twice its size, so a completed line overshoots the target. And a dozen wins only 12 times in 37, about 32.4% of spins, which is just under one in three.

That second number matters more than it looks. A line clears when wins remove numbers faster than losses add them, and with two numbers off per win and one on per loss, the break-even win rate is one in three. On a dozen, the expected change in the line’s length is slightly positive on every bet: minus two numbers 32.4% of the time, plus one number 67.6% of the time, a drift of about +0.03 numbers per spin. So on a dozen, the line tends to grow. Cycles still complete often enough to feel normal, but they run longer and reach high stakes more easily. The house edge per bet is unchanged at 2.70%.

Tuning the line

Players adjust the line to taste. A short line of small numbers, such as 1-1-1, targets only 3 units and rarely reaches the table limit. A long line like 1-2-3-4-5-6 targets 21 units, starts at 7 units a bet and grows faster on a losing run. Some split a long line into two short ones to keep stakes down. All of these change how often the limit is reached and what a completed line pays. None changes the price of each bet.

The reverse Labouchère flips the bookkeeping: add numbers after wins, cross them off after losses. Losses are capped at the line’s total, and a long winning streak can run far. It is the mirror image in every respect except cost.

Before you write a line

Pick the target from what you are prepared to spend on a session, then pick the unit, never the other way round. Set a money limit and a time limit, stop at whichever comes first, and do not start a new, larger line to make up an unfinished one. The bankroll and session limits guide has sample budgets, and the responsible gambling page lists limit tools and support lines by province.

Check the table limits as well. Live tables put their minimum and maximum on screen, and the live roulette guide explains what Canadian players will find there. A table with a narrow spread between minimum and maximum leaves a Labouchère line very little room.

Henry Labouchère, for what it is worth, was better known in his day for founding the magazine Truth and for a long career as a Radical MP than for anything he did at a roulette table. His name survives at the casino table all the same, mostly on scraps of paper covered in crossed-out numbers.